The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.
In nuclear power plants, core monitoring systems provide a controlled environment for processing raw plant data into operational limiting data such as maximum heat generation rate. Such systems monitor key reactor state information, such as margins to operating limits, axial and radial power, exposure distributions, total core power to provide information to evaluate past, current and future fuel performance. Additionally, such systems are often used to prepare plans for future operations, such as control rod sequence exchanges, startups, and power maneuvers, of the reactor based on the monitored data. The system can receive user input related to planned operations and can generate models and operational characteristics and plans in support of the planned operation. This can include simulations of the planned operation based on predefined and/or calculated operational parameters and characteristics. A core simulator can calculate current, expected, and planned neutron flux, power distributions, thermal performance as a function of control rod position, core loading pattern, coolant flow, reactor pressure, and other operational and design variables.
One of the most important reported reactor parameters is a ratio of the neutron gain to neutron loss sometimes referred to as the effective neutron multiplication factor, critical effective k, or critical k-eigenvalue, each of the terms being used interchangeably herein. This is the ratio of the average rate of neutron production by fission in the reactor core to the average rate of loss by absorption and leakage. The effective k is a constant that gives the information about the current state of the chain reaction or fission in the core. A value of effective k less than one indicates a decreasing number of chain reactions, whereas a value of the effective k greater than one indicates an increasing number of chain reactions at the current state of the reactor. A self-sustaining steady state reactor state is called the critical state of the reactor and theoretically in a steady state has a effective k equal to one. Unfortunately, due to uncertainties associated with the reactor data and the methodology to calculate the quantities, the effective k is not always equal to one. This special value of effective k is called the critical effective k.
During the planning stage of a reactor operation the reactors experience conditions that are below full power reactor conditions, referred to herein as off-rated conditions or operations that include control rod sequence exchanges, startups or power maneuvers from which reactor engineers prepare an operational plan for the reactor operators. Each off-rated condition places the reactor in a plurality of off-rated core states wherein the rate of neutron generation is increasing or decreasing differently than at full power, e.g., an effective k that is not equal to one. Reactor plans for off-rated conditions typically include calculating an estimate of the coolant flow rate at every stage of the operation for the targeted power level and the control rod pattern. The process is almost the reverse of the effective k calculation. The core systems support this process by providing predictions based on predefined rules and past operating data. The accuracy of the calculated coolant flow rate is important for reaching the targeted power level as fast as the regulated thermal limits will allow. A poor estimate of the flow rate results in small conservative increments in the flow rate necessary to reach the targeted power, which can result in increased time and expense to reach full power. A good estimate of the expected critical effective k for each state point in the off-rated condition will provide for more accurate predictions of coolant flow rate and optimized operation of the reactor.
However, typically either the design basis effective k or the rated last known effective k is used for flow calculations due to the current inability to accurately predict an expected critical effective k. Because the critical effective k is not a constant value it has been very difficult to predict because it is a function of the complex interaction of all parameters affecting the operation of the reactor core. The critical effective k can decrease as the cycle progresses and can change by about 600 pcm (percent-mille-reactivity) during the each fuel load cycle life time at full power rated conditions. This change is approximately piecewise linear and can be predicted by a design basis effective k. As the critical effective k changes as a function of the burnup, it can also change as much 700 pcm during these off rated conditions. The design effective k is calculated during the design process of the new refueled core and is expected to have an accuracy of 200 pcm. However, the design effective k does not address the off rated conditions where power is below 100%.
The determination of the flow rate is sensitive to the selected critical effective k and a 50 pcm difference in the critical effective k from that predicted can result in 2% difference in the flow rate. Consequently, employment of the design basis effective k or the last known value of the rated conditions critical effective k can produce as large as a 25% difference between the calculated and the actual flow rate during these off-rated power states.
Therefore, a prediction methodology to improve the calculation of an accurate critical effective k during off rated states and conditions is desired in order to optimize the operation of the reactor while maintaining desired safety margins.